where \(\mathcal {D}_{l}\)  and \(\mathcal {D}_{u}\)  denote the labeled and unlabeled data sets, respectively, and \(\alpha \)  is a coefficient that controls the relative importance of classification loss.
By optimizing the loss function of the Semi-VAE, the model can be aware of the relatedness between label prediction and input data reconstruction, which can help exploit useful information of unlabeled data to alleviate the scarcity problem of labeled training data.
However, Semi-VAE cannot be directly applied to semi-supervised adversarial learning, because in adversarial learning the discriminator cannot accurately infer the sensitive attributes from hidden representations and thereby cannot help input data reconstruction.
To solve this problem, we propose an adversarial semi-supervised variational autoencoder based on decomposed adversarial learning [1]}, which can mine the relatedness between input data reconstruction and the sensitive attributes predicted by a bias-aware model and meanwhile encourage the bias-free model to be less attribute discriminative.
